Problem: One day mum asked Petya to sort his toys and get rid of some of them. Petya found a whole box of toy spiders. They were quite dear to him and the boy didn't want to throw them away. Petya conjured a cunning plan: he will glue all the spiders together and attach them to the ceiling. Besides, Petya knows that the lower the spiders will hang, the more mum is going to like it and then she won't throw his favourite toys away. Help Petya carry out the plan.

A spider consists of k beads tied together by k - 1 threads. Each thread connects two different beads, at that any pair of beads that make up a spider is either directly connected by a thread, or is connected via some chain of threads and beads.

Petya may glue spiders together directly gluing their beads. The length of each thread equals 1. The sizes of the beads can be neglected. That's why we can consider that gluing spiders happens by identifying some of the beads (see the picture). Besides, the construction resulting from the gluing process should also represent a spider, that is, it should have the given features. 

After Petya glues all spiders together, he measures the length of the resulting toy. The distance between a pair of beads is identified as the total length of the threads that connect these two beads. The length of the resulting construction is the largest distance between all pairs of beads. Petya wants to make the spider whose length is as much as possible.

<image> <image>

The picture two shows two spiders from the second sample. We can glue to the bead number 2 of the first spider the bead number 1 of the second spider. The threads in the spiders that form the sequence of threads of maximum lengths are highlighted on the picture.

Input

The first input file line contains one integer n (1 ≤ n ≤ 100) — the number of spiders. Next n lines contain the descriptions of each spider: integer ni (2 ≤ ni ≤ 100) — the number of beads, then ni - 1 pairs of numbers denoting the numbers of the beads connected by threads. The beads that make up each spider are numbered from 1 to ni.

Output

Print a single number — the length of the required construction.

Examples

Input

1
3 1 2 2 3


Output

2


Input

2
3 1 2 1 3
4 1 2 2 3 2 4


Output

4


Input

2
5 1 2 2 3 3 4 3 5
7 3 4 1 2 2 4 4 6 2 7 6 5


Output

7

Solution (in JAVA):

Solution:
import java.io.InputStream;
import java.io.FileOutputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.FileInputStream;
import java.io.InputStream;
import java.io.BufferedWriter;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.OutputStream;
/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Alex
 */
public class Main{
	public static void main(String[] args){
		InputStream inputStream;
		try{
			inputStream = new FileInputStream("input.txt");
		} catch(IOException e){
			throw new RuntimeException(e);
		}
		OutputStream outputStream;
		try{
			outputStream = new FileOutputStream("output.txt");
		} catch(IOException e){
			throw new RuntimeException(e);
		}
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskF solver = new TaskF();
		solver.solve(1, in, out);
		out.close();
	}
	static class TaskF{
		public void solve(int testNumber, InputReader in, OutputWriter out){
			int n = in.ri();
			int res = 0;
			for(int spider = 0; spider < n; spider++) res += getlen(in);
			out.printLine(res);
		}
		int getlen(InputReader in){
			int n = in.ri();
			BidirectionalGraph g = new BidirectionalGraph(n);
			for(int edge = 0; edge < n - 1; edge++) {
				g.addWeightedEdge(in.ri() - 1, in.ri() - 1, 1);
			}
			long res = 0;
			for(int start = 0; start < n; start++) {
				Pair<long[], int[]> temp = ShortestDistance.dijkstraAlgorithm(g, start);
				for(long val : temp.first) {
					res = Math.max(res, val);
				}
			}
			return (int) res;
		}
	}
	static class Pair<U, V> implements Comparable<Pair<U, V>>{
		public U first;
		public V second;
		public static <U, V> Pair<U, V> makePair(U first, V second){
			return new Pair<U, V>(first, second);
		}
		private Pair(U first, V second){
			this.first = first;
			this.second = second;
		}
		public boolean equals(Object o){
			if(this == o) return true;
			if(o == null || getClass() != o.getClass()) return false;
			Pair pair = (Pair) o;
			return !(first != null ? !first.equals(pair.first) : pair.first != null) && !(second != null ? !second.equals(pair.second) : pair.second != null);
		}
		public int hashCode(){
			int result = first != null ? first.hashCode() : 0;
			result = 31 * result + (second != null ? second.hashCode() : 0);
			return result;
		}
		public String toString(){
			return "(" + first + "," + second + ")";
		}
		@SuppressWarnings({"unchecked"})
		public int compareTo(Pair<U, V> o){
			int value = ((Comparable<U>) first).compareTo(o.first);
			if(value != 0)
				return value;
			return ((Comparable<V>) second).compareTo(o.second);
		}
	}
	static class Graph{
		public static final int REMOVED_BIT = 0;
		protected int vertexCount;
		protected int edgeCount;
		private int[] firstOutbound;
		private int[] firstInbound;
		private Edge[] edges;
		private int[] nextInbound;
		private int[] nextOutbound;
		private int[] from;
		private int[] to;
		private long[] weight;
		public long[] capacity;
		private int[] reverseEdge;
		private int[] flags;
		public Graph(int vertexCount){
			this(vertexCount, vertexCount);
		}
		public Graph(int vertexCount, int edgeCapacity){
			this.vertexCount = vertexCount;
			firstOutbound = new int[vertexCount];
			Arrays.fill(firstOutbound, -1);
			from = new int[edgeCapacity];
			to = new int[edgeCapacity];
			nextOutbound = new int[edgeCapacity];
			flags = new int[edgeCapacity];
		}
		public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge){
			ensureEdgeCapacity(edgeCount + 1);
			if(firstOutbound[fromID] != -1)
				nextOutbound[edgeCount] = firstOutbound[fromID];
			else
				nextOutbound[edgeCount] = -1;
			firstOutbound[fromID] = edgeCount;
			if(firstInbound != null){
				if(firstInbound[toID] != -1)
					nextInbound[edgeCount] = firstInbound[toID];
				else
					nextInbound[edgeCount] = -1;
				firstInbound[toID] = edgeCount;
			}
			this.from[edgeCount] = fromID;
			this.to[edgeCount] = toID;
			if(capacity != 0){
				if(this.capacity == null)
					this.capacity = new long[from.length];
				this.capacity[edgeCount] = capacity;
			}
			if(weight != 0){
				if(this.weight == null)
					this.weight = new long[from.length];
				this.weight[edgeCount] = weight;
			}
			if(reverseEdge != -1){
				if(this.reverseEdge == null){
					this.reverseEdge = new int[from.length];
					Arrays.fill(this.reverseEdge, 0, edgeCount, -1);
				}
				this.reverseEdge[edgeCount] = reverseEdge;
			}
			if(edges != null)
				edges[edgeCount] = createEdge(edgeCount);
			return edgeCount++;
		}
		protected final Graph.GraphEdge createEdge(int id){
			return new Graph.GraphEdge(id);
		}
		public final int addFlowWeightedEdge(int from, int to, long weight, long capacity){
			if(capacity == 0){
				return addEdge(from, to, weight, 0, -1);
			} else{
				int lastEdgeCount = edgeCount;
				addEdge(to, from, -weight, 0, lastEdgeCount + entriesPerEdge());
				return addEdge(from, to, weight, capacity, lastEdgeCount);
			}
		}
		protected int entriesPerEdge(){
			return 1;
		}
		public final int addWeightedEdge(int from, int to, long weight){
			return addFlowWeightedEdge(from, to, weight, 0);
		}
		public final int vertexCount(){
			return vertexCount;
		}
		protected final int edgeCapacity(){
			return from.length;
		}
		public final int firstOutbound(int vertex){
			int id = firstOutbound[vertex];
			while(id != -1 && isRemoved(id))
				id = nextOutbound[id];
			return id;
		}
		public final int nextOutbound(int id){
			id = nextOutbound[id];
			while(id != -1 && isRemoved(id))
				id = nextOutbound[id];
			return id;
		}
		public final int destination(int id){
			return to[id];
		}
		public final long weight(int id){
			if(weight == null)
				return 0;
			return weight[id];
		}
		public final boolean flag(int id, int bit){
			return (flags[id] >> bit & 1) != 0;
		}
		public final boolean isRemoved(int id){
			return flag(id, REMOVED_BIT);
		}
		protected void ensureEdgeCapacity(int size){
			if(from.length < size){
				int newSize = Math.max(size, 2 * from.length);
				if(edges != null)
					edges = resize(edges, newSize);
				from = resize(from, newSize);
				to = resize(to, newSize);
				nextOutbound = resize(nextOutbound, newSize);
				if(nextInbound != null)
					nextInbound = resize(nextInbound, newSize);
				if(weight != null)
					weight = resize(weight, newSize);
				if(capacity != null)
					capacity = resize(capacity, newSize);
				if(reverseEdge != null)
					reverseEdge = resize(reverseEdge, newSize);
				flags = resize(flags, newSize);
			}
		}
		protected final int[] resize(int[] array, int size){
			int[] newArray = new int[size];
			System.arraycopy(array, 0, newArray, 0, array.length);
			return newArray;
		}
		private long[] resize(long[] array, int size){
			long[] newArray = new long[size];
			System.arraycopy(array, 0, newArray, 0, array.length);
			return newArray;
		}
		private Edge[] resize(Edge[] array, int size){
			Edge[] newArray = new Edge[size];
			System.arraycopy(array, 0, newArray, 0, array.length);
			return newArray;
		}
		public final boolean isSparse(){
			return vertexCount == 0 || edgeCount * 20 / vertexCount <= vertexCount;
		}
		protected class GraphEdge implements Edge{
			protected int id;
			protected GraphEdge(int id){
				this.id = id;
			}
		}
	}
	static interface IntComparator{
		public static final IntComparator DEFAULT = new IntComparator(){
			public int compare(int first, int second){
				if(first < second)
					return -1;
				if(first > second)
					return 1;
				return 0;
			}
		};
		public int compare(int first, int second);
	}
	static class OutputWriter{
		private final PrintWriter writer;
		public OutputWriter(OutputStream outputStream){
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
		public OutputWriter(Writer writer){
			this.writer = new PrintWriter(writer);
		}
		public void close(){
			writer.close();
		}
		public void printLine(int i){
			writer.println(i);
		}
	}
	static class IntegerUtils{
		public static int longCompare(long a, long b){
			if(a < b)
				return -1;
			if(a > b)
				return 1;
			return 0;
		}
	}
	static class Heap{
		private IntComparator comparator;
		private int size = 0;
		private int[] elements;
		private int[] at;
		public Heap(int maxElement){
			this(10, maxElement);
		}
		public Heap(IntComparator comparator, int maxElement){
			this(10, comparator, maxElement);
		}
		public Heap(int capacity, int maxElement){
			this(capacity, IntComparator.DEFAULT, maxElement);
		}
		public Heap(int capacity, IntComparator comparator, int maxElement){
			this.comparator = comparator;
			elements = new int[capacity];
			at = new int[maxElement];
			Arrays.fill(at, -1);
		}
		public boolean isEmpty(){
			return size == 0;
		}
		public int add(int element){
			ensureCapacity(size + 1);
			elements[size] = element;
			at[element] = size;
			shiftUp(size++);
			return at[element];
		}
		public void shiftUp(int index){
//		if (index < 0 || index >= size)
//			throw new IllegalArgumentException();
			int value = elements[index];
			while(index != 0){
				int parent = (index - 1) >>> 1;
				int parentValue = elements[parent];
				if(comparator.compare(parentValue, value) <= 0){
					elements[index] = value;
					at[value] = index;
					return;
				}
				elements[index] = parentValue;
				at[parentValue] = index;
				index = parent;
			}
			elements[0] = value;
			at[value] = 0;
		}
		public void shiftDown(int index){
			if(index < 0 || index >= size)
				throw new IllegalArgumentException();
			while(true){
				int child = (index << 1) + 1;
				if(child >= size)
					return;
				if(child + 1 < size && comparator.compare(elements[child], elements[child + 1]) > 0)
					child++;
				if(comparator.compare(elements[index], elements[child]) <= 0)
					return;
				swap(index, child);
				index = child;
			}
		}
		public int getIndex(int element){
			return at[element];
		}
		private void swap(int first, int second){
			int temp = elements[first];
			elements[first] = elements[second];
			elements[second] = temp;
			at[elements[first]] = first;
			at[elements[second]] = second;
		}
		private void ensureCapacity(int size){
			if(elements.length < size){
				int[] oldElements = elements;
				elements = new int[Math.max(2 * elements.length, size)];
				System.arraycopy(oldElements, 0, elements, 0, this.size);
			}
		}
		public int poll(){
			if(isEmpty())
				throw new IndexOutOfBoundsException();
			int result = elements[0];
			at[result] = -1;
			if(size == 1){
				size = 0;
				return result;
			}
			elements[0] = elements[--size];
			at[elements[0]] = 0;
			shiftDown(0);
			return result;
		}
	}
	static class InputReader{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private InputReader.SpaceCharFilter filter;
		public InputReader(InputStream stream){
			this.stream = stream;
		}
		public int read(){
			if(numChars == -1)
				throw new InputMismatchException();
			if(curChar >= numChars){
				curChar = 0;
				try{
					numChars = stream.read(buf);
				} catch(IOException e){
					throw new InputMismatchException();
				}
				if(numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}
		public int ri(){
			return readInt();
		}
		public int readInt(){
			int c = read();
			while(isSpaceChar(c))
				c = read();
			int sgn = 1;
			if(c == '-'){
				sgn = -1;
				c = read();
			}
			int res = 0;
			do{
				if(c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while(!isSpaceChar(c));
			return res * sgn;
		}
		public boolean isSpaceChar(int c){
			if(filter != null)
				return filter.isSpaceChar(c);
			return isWhitespace(c);
		}
		public static boolean isWhitespace(int c){
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		public interface SpaceCharFilter{
			public boolean isSpaceChar(int ch);
		}
	}
	static class ShortestDistance{
		public static Pair<long[], int[]> dijkstraAlgorithm(Graph graph, int source){
			int vertexCount = graph.vertexCount();
			final long[] distance = new long[vertexCount];
			int[] last = new int[vertexCount];
			Arrays.fill(distance, Long.MAX_VALUE);
			Arrays.fill(last, -1);
			distance[source] = 0;
			if(graph.isSparse()){
				Heap heap = new Heap(vertexCount, new IntComparator(){
					public int compare(int first, int second){
						return IntegerUtils.longCompare(distance[first], distance[second]);
					}
				}, vertexCount);
				heap.add(source);
				while(!heap.isEmpty()){
					int current = heap.poll();
					int id = graph.firstOutbound(current);
					while(id != -1){
						int next = graph.destination(id);
						long total = graph.weight(id) + distance[current];
						if(distance[next] > total){
							distance[next] = total;
							if(heap.getIndex(next) == -1)
								heap.add(next);
							else
								heap.shiftUp(heap.getIndex(next));
							last[next] = id;
						}
						id = graph.nextOutbound(id);
					}
				}
			} else{
				boolean[] visited = new boolean[vertexCount];
				for(int i = 0; i < vertexCount; i++) {
					int index = -1;
					long length = Long.MAX_VALUE;
					for(int j = 0; j < vertexCount; j++) {
						if(!visited[j] && distance[j] < length){
							length = distance[j];
							index = j;
						}
					}
					if(index == -1)
						break;
					visited[index] = true;
					int id = graph.firstOutbound(index);
					while(id != -1){
						int next = graph.destination(id);
						if(!visited[next]){
							long total = graph.weight(id) + length;
							if(distance[next] > total){
								distance[next] = total;
								last[next] = id;
							}
						}
						id = graph.nextOutbound(id);
					}
				}
			}
			return Pair.makePair(distance, last);
		}
	}
	static interface Edge{
	}
	static class BidirectionalGraph extends Graph{
		public int[] transposedEdge;
		public BidirectionalGraph(int vertexCount){
			this(vertexCount, vertexCount);
		}
		public BidirectionalGraph(int vertexCount, int edgeCapacity){
			super(vertexCount, 2 * edgeCapacity);
			transposedEdge = new int[2 * edgeCapacity];
		}
		public int addEdge(int fromID, int toID, long weight, long capacity, int reverseEdge){
			int lastEdgeCount = edgeCount;
			super.addEdge(fromID, toID, weight, capacity, reverseEdge);
			super.addEdge(toID, fromID, weight, capacity, reverseEdge == -1 ? -1 : reverseEdge + 1);
			this.transposedEdge[lastEdgeCount] = lastEdgeCount + 1;
			this.transposedEdge[lastEdgeCount + 1] = lastEdgeCount;
			return lastEdgeCount;
		}
		protected int entriesPerEdge(){
			return 2;
		}
		protected void ensureEdgeCapacity(int size){
			if(size > edgeCapacity()){
				super.ensureEdgeCapacity(size);
				transposedEdge = resize(transposedEdge, edgeCapacity());
			}
		}
	}
}